The goal of our experiment is to determine how different
weights affect the launch distance in catapults. Keeping the launch angle the
same, at 45 degrees, and the length of the sling the same, we will determine
what the most effective weight will be, and how varying from that weight affects
the distance of the launch. Our hypothesis is that very light weights will not
go very far due to wind resistance and a lack of momentum, and very heavy
weights will also fly short because of the heightened amount of force needed to
move them at all. There will be some weight in the middle that will be a happy
medium, depending on the size of the catapult and the force it can generate to
propel the ping pong ball.

The desire for catapults stems from mankind’s consistent
drive to make warfare a more mechanical practice. The concept of a catapult is
quite simple, projecting a heavy or abnormal object a very far distance, yet
human limitations required a mechanized solution. The first recorded historical
reference to siege weapons goes back to “A.D. 339 when a biographer states
that Dionysos I, Tyrant of Syracuse, brought together engineers from all over
the Mediterranean for the purpose of developing an engine of war powered by a
large bow - requiring more power than one man could muster” (Peter Hansen).
Later, the “Romans adopted the torsion artillery invented by Greek
engineers” and would successively use them in battle during the peak years of
their empire (Alan Wilkins). The prosperity the catapult would have in battle
became evident as, “The first weapons using gunpowder were introduced to the
theatres of war in Europe during the 14th century but it took another 200 years
before they replaced the old engines of war completely”(Hansen). Yet the
concept of catapults today still has a variety of uses.

The modern day uses of catapults has evolved considerably
from its origins of using a simple bow to launch an arrow into being implemented
onto air craft carriers as a means of providing enough velocity to fighter jets
to gain the necessary lift for takeoff. Although there are several different
technologies that fall into the "catapult" category including the
catapult, the ballista and the trebuchet, all three attempts to use stored
potential energy rapidly converted into kinetic to propel heavy objects long
distances. Both catapults and ballistas work by storing tension either in
twisted ropes or in a flexed piece of wood. This is where a trebuchet differs,
as it tends to consists simply of a pivoting beam and a counterweight that
rotates the beam through an arc (see attached diagrams). Depending on the size
and strength of materials used, a catapult’s capacity to thrust objects can
range up to a thousand feet (HSW).

This data supports our original hypothesis of finding a
"happy medium" for the projectile weight. First starting out with the
lighter ping-pong balls, we were getting short distances because of wind
resistance on the balls. The 11.32-gram ball, for instance, only went an average
distance of 15.80 meters. At this point, increasing the weight of the ping-pong
balls generally made them launch farther. Overall, the 28.35-gram ping-pong ball
went the farthest, with an average distance of 29.75 meters. After adding even
more weight, the distances of the launches began to decline, eventually
concluding with a 65.26-gram ping-pong ball traveling an average distance of
24.60 meters. This shows that our "happy medium" for our particular
catapult is around 28 grams for a ping-pong ball sized projectile. To improve
the experiment, a launch device instead of a sling, or a different type of
catapult could be used. The experiment could also be done indoors where the
variables such as the wind could be controlled. Possibly more trials could also
produce more clear distinctions between masses, especially between the 50, 75,
and 100 balls. Overall, the experiment yielded the expected results of a
correlation between the mass of the projectiles and their launch distance from
the catapult.

There are certain almost unavoidable uncertainties in
dealing with outside trials. The main uncertainty presented by an outside
project is the wind. Because the trials were all performed within the same
couple of hours, and the wind fluctuates noticeably, it is almost definitely a
cause of uncertainty in the data. During the trials the wind felt about 5 to 7
mph in the direction of the launches at some points, and then non-existent at
other times. This may have accounted for some inconsistencies, but not enough to
have skewed the data significantly. There also was the human error in
determining exactly where the balls landed. Although there was snow on the
ground, and the balls made marks in the snow, sometimes it was difficult to
determine exactly where it landed because of footprints, etc. The final source
of significant uncertainty in the data was present in the setup of the catapult
for each trial. The launches could have been slightly inconsistent due to the
inexact nature of the sling on the catapult. The sling and balls were set up in
almost the same exact position every time, but slings are not always exact, and
neither is the whole catapult mechanism necessarily. But, none of these
uncertainties appeared to alter the data in any totally significant manner
judging by the relative consistency of the data.

By far the best source for understanding the properties of
physics that give the catapult its unique ability, such as torsion. This online
library would be useful for just about any other research defense project.

Building a Catapult

http://www.glenn.cockwell.com/scouting/scouting_catapult1.html

This is a very good site in building a catapult. We might
build a catapult of buy a kit to make one, but this site gives good instructions
on how to build one from scratch if we do. We could change the dimensions or
sizes of pieces if we wanted to.